Respected magazine Vanity Fair claimed Ms Deng, who was divorced from her husband last year, wrote of her admiration for the former Prime Minister’s piercing “blue eyes”.

The undated note mentions her apparently “so missing” Mr Blair because he was “charming”, “his clothes are so good” and because of his “power on the stage”.

It was purportedly written by Ms Deng, 44, and found after her media tycoon husband, 82, found out the former Prime Minister had allegedly spent weekends at his homes.

Writing in broken English, the author exclaimed: “Oh, shit, oh, shit. Whatever why I’m so so missing Tony. Because he is so so charming and his clothes are so good.

“He has such good body and he has really really good legs Butt... And he is slim tall and good skin. Pierce blue eyes which I love.

“Love his eyes. Also I love his power on the stage... and what else and what else and what else ...”

Mr Murdoch and Ms Deng were divorced last year after 14 years of marriage. There is no evidence that Mr Blair’s friendship with Ms Deng was a factor.

Sources close to Mr Blair have said any claims of a relationship going beyond a friendship were “completely untrue”. Vanity Fair’s latest issue contains a detailed article quoting sources described as having direct knowledge of the marriage breakdown.

The source told the US magazine: “She would make up an excuse to be somewhere. She would say she’s going up to the ranch in Carmel with a girlfriend.” The source claimed that staff gave Mr Murdoch detailed accounts of his wife’s meetings.

The magazine quoted someone who "worked in a Murdoch family home" as saying: "They were all mutual friends; there was no reason Mr Murdoch wouldn't have welcomed Mr Blair into his home."

Last year Mr Murdoch and Ms Deng said they had decided “not to engage in public allegations or respond to negative claims.”

Mr Blair, who is godfather to one of Mr Murdoch and Miss Deng's children, was on close terms with the media tycoon.